Cyclides in computer aided geometric design
Computer Aided Geometric Design
Modeling arbitrary smooth objects with algebraic surfaces
Modeling arbitrary smooth objects with algebraic surfaces
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Cyclides in Surface and Solid Modeling
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Cubicoids: Modeling and visualization
Computer Aided Geometric Design
The NURBS book
Cyclides in computer aided geometric design II
Computer Aided Geometric Design
Blending with affine and projective Dupin cyclides
Neural, Parallel & Scientific Computations - computer aided geometric design
Computer Aided Geometric Design
Quartic supercyclides I: basic theory
Computer Aided Geometric Design
Computer Aided Geometric Design
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Surfaces: Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
Constructive shell representations for freeform surfaces and solids
IEEE Computer Graphics and Applications
Dupin Cyclides and Supercyclides
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Obtaining implicit equations of supercyclides and definition of elliptic supercyclides
Machine Graphics & Vision International Journal
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Most commercial CAD systems use parametric representations (e.g., NURBS) for defining free-form shapes. This leads to significant problems in certain types of geometric computation, and also in the exchange of CAD models between different systems. The paper suggests that there are good reasons for developing alternative approaches to the representation of free-form shapes in CAD, based on the use of algebraic surfaces. Work in this direction is currently at an early stage, but some significant research direction is currently at an early stage, but some significant research directions are being identified. The paper surveys the current state of the art, and indicates some fruitful areas for future work.